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inside the ".cmu.edu" domain.

visual displays of means and variances 
for subject 02882:
mean,
var,
stdev
 for subject 02930:
mean,
var,
stdev

Using neural network to predict left broca(t+1) from left broca(t).Initial
results show the average RMS error for neural net is 35.1, compared
to 47.3 when using voxel mean as the prediction, and 44.7 when using the
previous voxel value as the prediction.
More detailed results on a later
run include the partial derivatives of the predictions.

Using linear regression to predict left broca(t) from left broca(t1,..,tN).
N varies from 1 to 10.Results show that the
RMS error on the testing set varies from 36.0 to 79.6 as the width of the
time window goes from 1 up to 10, when absolute values are predicted from
absolute values. Best results are achieved for small time windows. Similar
results are achived when predicting the first difference of the signal
from a window of timelagged first differences. The best overall result
of 38.4 is obtained with time window of three.
A comparison between typical true and predicted results for linear
regression on the training set is shown below. The prediction was
based on a time window of size three.
The same comparison for the corresponding testing set:

Using k nearest neighbors to predict left broca(t) from left broca(t1,..,tN).
N varies from 1 to 10, and k varies from 1 to 7. Results
show
the best RMS error is achieved when predicting absolute values, and for
small time windows and as many nearest neighbors as possible. The best
result is 38.9, for N=2 and k=7. In contrast, predicting first differences
with kNN did not perform well  the best result was 56.8, again for N=2
and k=7.
These results can be compared against two baselines
:
using the mean as prediction and using the previous value in the time series.
The mean value yielded a high RMSE of 49.2. When using the most recent
value as a predictor, the error was somewhat lower (45.5), but not by a
lot.

More detailed results on
regression This
chart shows the performance of linear regression when predicting absolute
values of the fifteen voxels in left Broca with a window of three time
slices. Of those fifteen voxels, eight are linearly predictable, while
the other seven are not.
The regression coefficients are visualized in the image below.
Black corresponds to negative and white corresponds to positive coefficients.
A pixel with coordinates (x,y), counted from the upper left corner of the
image, corresponds to the coefficient relating input x to output y  that
is, the image corresponds to a Jacobian matrix in its layout. The time
delayed vector of inputs has time slice tN to the left and time slice
t1 to the right.
The image below shows the correlation matrix of the activation signals
of the fifteen voxels in left Broca. White color corresponds to strong
positive correlation, and black to no (zero) correlation.

Using neural network to predict lb,lt(t+1) from lb,lt(t).Initial
results . RMS prediction error 33.31, compared to 41.45 using means
to predict.

Using neural network to predict lt(t+1) from lb(t).Initial
results . RMS prediction error 31.82, compared to 39.07 using means
to predict.

Using neural network to predict lb(t+1) from lt(t).Initial
results RMS prediction error 38.89, compared to 47.1 using means to
predict.
Predicting lb(t+1) from lb(t) for 02882  PP&RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
35.4030 
35.3599 
kernel regression 
36.7323 
44.2866 
k nearest neighbors 
37.6975 
40.3757 
latest value 
44.3493 
44.3493 
mean value 
47.9650 
47.9650 
Predicting lb(t+1) from lb(t) for 02882  PP
Method 
Error on raw data 
Error on percentages 
linear regression 
36.9842 
37.1254 
kernel regression 
37.1057 
44.2537 
k nearest neighbors 
37.8392 
40.1486 
latest value 
44.2351 
44.2351 
mean value 
46.8361 
46.8361 
Predicting lb(t+1) from lb(t) for 02882  RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
37.3158 
37.3919 
kernel regression 
38.4470 
44.9196 
k nearest neighbors 
38.3039 
40.8477 
latest value 
44.4042 
44.4042 
mean value 
47.3010 
47.3010 
Predicting lt(t+1) from lt(t) for 02882  PP&RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
31.2933 
31.1898 
kernel regression 
31.2634 
33.4739 
k nearest neighbors 
32.0502 
40.3757 
latest value 
38.5323 
38.5323 
mean value 
39.8031 
39.8031 
Predicting lt(t+1) from lt(t) for 02882  PP
Method 
Error on raw data 
Error on percentages 
linear regression 
34.2106 
34.1594 
kernel regression 
31.8218 
37.0377 
k nearest neighbors 
32.2334 
34.2376 
latest value 
39.0910 
39.0910 
mean value 
39.3279 
39.3279 
Predicting lt(t+1) from lt(t) for 02882  RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
34.1592 
33.8042 
kernel regression 
31.9268 
35.8551 
k nearest neighbors 
31.5950 
33.1942 
latest value 
38.2995 
38.2995 
mean value 
37.5290 
37.5290 
Predicting lb,lt(t+1) from lb,lt(t) for 02882  PP&RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
32.9781 
32.9912 
kernel regression 
32.9026 
38.3856 
k nearest neighbors 
33.4124 
34.7364 
latest value 
40.2931 
40.2931 
mean value 
42.3672 
42.3672 
Predicting lb,lt(t+1) from lb,lt(t) for 02882  PP
Method 
Error on raw data 
Error on percentages 
linear regression 
36.6374 
36.5897 
kernel regression 
33.5188 
38.6737 
k nearest neighbors 
33.2764 
35.0448 
latest value 
40.6927 
40.6927 
mean value 
41.7719 
41.7719 
Predicting lb,lt(t+1) from lb,lt(t) for 02882  RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
37.4406 
37.3416 
kernel regression 
33.8780 
38.2591 
k nearest neighbors 
33.1496 
34.6820 
latest value 
40.2573 
40.2573 
mean value 
40.6477 
40.6477 
Predicting lb(t+1) from lb(t) for 02930  PP&RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
36.0740 
36.0824 
kernel regression 
35.5461 
39.0011 
k nearest neighbors 
36.2593 
38.3240 
latest value 
44.5436 
44.5436 
mean value 
40.2094 
40.2094 
Predicting lb(t+1) from lb(t) for 02930  PP
Method 
Error on raw data 
Error on percentages 
linear regression 
37.6649 
37.7794 
kernel regression 
36.4024 
38.8822 
k nearest neighbors 
36.3552 
38.0757 
latest value 
43.9044 
43.9044 
mean value 
39.0530 
39.0530 
Predicting lb(t+1) from lb(t) for 02930  RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
36.4076 
36.5440 
kernel regression 
35.7675 
38.1737 
k nearest neighbors 
36.4065 
38.1637 
latest value 
44.3173 
44.3173 
mean value 
38.2857 
38.2857 
Predicting lt(t+1) from lt(t) for 02930  PP&RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
32.6557 
32.6441 
kernel regression 
33.0032 
36.3991 
k nearest neighbors 
33.9985 
37.2002 
latest value 
38.5323 
38.5323 
mean value 
36.9298 
36.9298 
Predicting lt(t+1) from lt(t) for 02930  PP
Method 
Error on raw data 
Error on percentages 
linear regression 
33.1444 
33.0677 
kernel regression 
33.4922 
36.1160 
k nearest neighbors 
32.7904 
35.5905 
latest value 
40.4429 
40.4429 
mean value 
36.2968 
36.2968 
Predicting lt(t+1) from lt(t) for 02930  RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
34.1112 
33.9552 
kernel regression 
33.1998 
35.5823 
k nearest neighbors 
34.0388 
36.9136 
latest value 
41.8895 
41.8895 
mean value 
35.5599 
35.5599 
Predicting lb,lt(t+1) from lb,lt(t) for 02930  PP&RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
34.7935 
34.8552 
kernel regression 
34.5333 
37.8808 
k nearest neighbors 
34.6222 
36.6398 
latest value 
43.4562 
43.4562 
mean value 
38.7148 
38.7148 
Predicting lb,lt(t+1) from lb,lt(t) for 02930  PP
Method 
Error on raw data 
Error on percentages 
linear regression 
37.4442 
37.4967 
kernel regression 
35.0515 
37.8006 
k nearest neighbors 
34.2027 
36.0388 
latest value 
42.6260 
42.6260 
mean value 
38.2030 
38.2030 
Predicting lb,lt(t+1) from lb,lt(t) for 02930  RRC
Method 
Error on raw data 
Error on percentages 
linear regression 
36.9964 
37.0235 
kernel regression 
34.5741 
37.0835 
k nearest neighbors 
35.1504 
37.2247 
latest value 
43.3474 
43.3474 
mean value 
37.2884 
37.2884 